Comparison of the accurate Kohn-Sham solution with the generalized gradient approximations (GGAs) for the SN2 reaction F-+CH3F→FCH3+F-:: A qualitative rule to predict success or failure of GGAs

Kohn-Sham solutions are constructed from ab initio densities obtained with multireference configuration interaction (MRCI) calculations for the transition state (TS) and for the intermediate complex (IC) of the prototype symmetrical S(N)2 reaction F- + CH3F --> FCH3 + F-. The calculated KS exchange and correlation energies, epsilon(x)(KS) and epsilon(c)(KS), as well as the exchange and exchange-correlation (xc) energy densities epsilon(x)(KS)(r) and epsilon(xc)(KS)(r), are compared with the corresponding quantities of the standard generalized gradient approximation (GGA). GGA functionals substantially underestimate the repulsive exchange contribution to the central barrier of the S(N)2 reaction, thus producing a too low barrier. A similar problem arises in a number of other bonding situations, and a qualitative rule is put forward to predict success or failure of standard GGAs in molecular calculations, depending on the type of chemical bonding. For systems with two-center two-electron bonds (standard covalent bonds), two-center four-electron Pauli repulsion (interacting closed shells), and three-center three-electron bonds, current GGAs (or minor modifications) are expected to perform successfully. In these cases the GGA exchange functional represents exchange and (if it is present) nondynamical Coulomb correlation, while the GGA correlation functional represents dynamical Coulomb correlation. Contrary to this, for systems with three-center four-electron bonds (TS of the S(N)2 reaction), two-center three-electron bonds, and two-center one-electron bonds, for which the exchange hole is delocalized over all interacting fragments and efficient nondynamical correlation is hampered by the unfavorable electron count, the GGA exchange functionals still yield nondynamical correlation, which is in these cases spurious, the GGAs thus overestimating the relative stability of these systems.